Let the speed of the train and bus be u and v respectively
Now According to the question,
And
Let,
Now, our equation becomes
And
By Cross Multiplication method,
And Hence,
Hence the speed of the train and bus are 60 km/hour and 80 km/hour respectively.

Let the number of days taken by woman and man be x and y respectively,
The proportion of Work done by a woman in a single day
The proportion of Work done by a man in a single day
Now, According to the question,
Also,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
So,

Given Equations,
As we can see by adding and subtracting both equations we can make our equations simple to solve.
So,
Adding (1) and )2) we get,
Subtracting (2) from (1) we get,
Now, Adding (3) and (4) we get,
Putting this value in (3)
Hence,
.

As we know that in a quadrilateral the sum of opposite angles is 180 degree.
So, From Here,
Also,
Multiplying (1) by 3 we get,
Now,
Subtracting, (2) from (3) we get,
Substituting this value in (1) we get,
Hence four angles of a quadrilateral are :

Given two equations,
And
Points(x,y) which satisfies equation (1) are:
X
0
1
5
Y
-5
0
20
Points(x,y) which satisfies equation (1) are:
X
0
1
2
Y
-3
0
3
GRAPH:
As we can see from the graph, the three points of the triangle are, (0,-3),(0,-5) and (1,0).

Let the speed of the train be v km/h and the time taken by train to travel the given distance be t hours and the distance to travel be d km.
Now As we Know,
Now, According to the question,
Now, Using equation (1), we have
Also,
Adding equations (2) and (3), we obtain:
Substituting the value of x in equation (2), we obtain:
Putting this value in (1) we get,
Hence...

Let the number of rows be x and number of students in a row be y.
Total number of students in the class = Number of rows * Number of students in a row
Now, According to the question,
Also,
Subtracting equation (2) from (1), we get:
Substituting the value of y in equation (1), we obtain:
Hence,
The number of rows is 4...

Let the age of Ani be , age of Biju be ,
Case 1: when Ani is older than Biju
age of Ani's father Dharam:
and
age of his sister Cathy :
Now According to the question,
Also,
Now subtracting (1) from (2), we get,
putting this in (1)
Hence the age of Ani and Biju is 19 years and 16 years respectively.
Case 2:
And
Now Adding (3) and (4), we get,
putting it in (3)
Hence the age of...

Let the speed of Ritu in still water be x and speed of current be y,
Let's solve this problem by using relative motion concept,
the relative speed when they are going in the same direction (downstream)= x +y
the relative speed when they are going in the opposite direction (upstream)= x - y
Now, As we know,
Relative distance = Relative speed * time .
So, According to the question,
And,
Now,...